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A223349 3X3X3 triangular graph without horizontal edges coloring a rectangular array: number of nX5 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

%I A223349 #6 Jul 23 2025 04:02:04
%S A223349 140,4908,202264,7918948,329268616,12912752876,537001573656,
%T A223349 21060038730884,875825392204488,34348003384801484,1428433095896220376,
%U A223349 56020099749013006372,2329712263359378360328,91366346681513601154476
%N A223349 3X3X3 triangular graph without horizontal edges coloring a rectangular array: number of nX5 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
%C A223349 Column 5 of A223352
%H A223349 R. H. Hardin, <a href="/A223349/b223349.txt">Table of n, a(n) for n = 1..210</a>
%F A223349 Empirical: a(n) = 1711*a(n-2) -132500*a(n-4) +3202240*a(n-6) -28936448*a(n-8) +102379520*a(n-10) -106561536*a(n-12) for n>13
%e A223349 Some solutions for n=3
%e A223349 ..1..0..2..4..1....0..1..0..2..5....4..1..4..1..3....0..2..0..2..4
%e A223349 ..3..1..0..2..0....1..4..2..5..2....1..3..1..0..1....2..0..2..4..2
%e A223349 ..1..0..2..0..2....0..1..0..2..0....0..1..4..1..0....0..2..4..2..5
%K A223349 nonn
%O A223349 1,1
%A A223349 _R. H. Hardin_ Mar 19 2013